Improved convergence of scattering calculations in the oscillator representation

The Schr\"odinger equation for two and tree-body problems is solved for scattering states in a hybrid representation where solutions are expanded in the eigenstates of the harmonic oscillator in the interaction region and on a finite difference grid in the near-- and far--field. The two representations are coupled through a high--order asymptotic formula that takes into account the function values and the third derivative in the classical turning points. For various examples the convergence is analyzed for various physics problems that use an expansion in a large number of oscillator states. The results show significant improvement over the JM-ECS method [Bidasyuk et al, Phys. Rev. C 82, 064603 (2010)]

An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg--Landau problem

This paper considers the extreme type-II Ginzburg--Landau equations, a nonlinear PDE model for describing the states of a wide range of superconductors. Based on properties of the Jacobian operator and an AMG strategy, a preconditioned Newton--Krylov method is constructed. After a finite-volume-type discretization, numerical experiments are done for representative two- and three-dimensional domains. Strong numerical evidence is provided that the number of Krylov iterations is independent of the dimension $n$ of the solution space, yielding an overall solver complexity of O(n)

A Microscopic Cluster Description of 12C

We investigate both bound and resonance states in 12C embedded in a three-\alpha-cluster continuum using two distinct three-cluster microscopic models. The first one relies on the Hyperspherical Harmonics basis to enumerate the channels describing the three-cluster continuum. The second model incorporates both Gaussian and Oscillator basis functions, and reduces the three-cluster problem to a two-cluster one, in which a two-cluster subsystem is described by a set of pseudo-bound state states. It is shown that the results agree well with comparable calculations from the literature.Comment: 31 pages, 12 figures, 9 table

Effective Hamiltonian and unitarity of the S matrix

The properties of open quantum systems are described well by an effective Hamiltonian ${\cal H}$ that consists of two parts: the Hamiltonian $H$ of the closed system with discrete eigenstates and the coupling matrix $W$ between discrete states and continuum. The eigenvalues of ${\cal H}$ determine the poles of the $S$ matrix. The coupling matrix elements $\tilde W_k^{cc'}$ between the eigenstates $k$ of ${\cal H}$ and the continuum may be very different from the coupling matrix elements $W_k^{cc'}$ between the eigenstates of $H$ and the continuum. Due to the unitarity of the $S$ matrix, the \TW_k^{cc'} depend on energy in a non-trivial manner, that conflicts with the assumptions of some approaches to reactions in the overlapping regime. Explicit expressions for the wave functions of the resonance states and for their phases in the neighbourhood of, respectively, avoided level crossings in the complex plane and double poles of the $S$ matrix are given.Comment: 17 pages, 7 figure